blender renders wrong portions of video strips
That's most likely a problem due to a broken Video file. The internally used ffmpeg libraries don't work too well with some video formats and are not able to always provide the frames without artifacts and in the right order one by one. I bet your Screencast software didn't do a good job in encoding your footage.

So try to repair your footage. And then instead of using RecordMyDesktop to capture your screen you should use Open Broadcaster Software recording to file, not LiveStream. It should provide you with non-problematic footage that you can use with Blender without problems.